• Title/Summary/Keyword: differential subordination

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SOME RESULTS ON CERTAIN CLASS OF ANALYTIC FUNCTIONS BASED ON DIFFERENTIAL SUBORDINATION

  • Prajapat, Jugal Kishore;Agarwal, Ritu
    • Bulletin of the Korean Mathematical Society
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    • v.50 no.1
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    • pp.1-10
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    • 2013
  • In the present paper we derive various useful properties and characteristics for certain class of analytic functions by using the techniques of differential subordination. Some interesting corollaries and applications of the results presented here are also discussed.

SEVEN-PARAMETER MITTAG-LEFFLER OPERATOR WITH SECOND-ORDER DIFFERENTIAL SUBORDINATION RESULTS

  • Maryam K. Rasheed;Abdulrahman H. Majeed
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.4
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    • pp.903-917
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    • 2023
  • This paper constructs a new linear operator associated with a seven parameters Mittag-Leffler function using the convolution technique. In addition, it investigates some significant second-order differential subordination properties with considerable sandwich results concerning that operator.

SOME SUBORDINATION PROPERTIES OF THE LINEAR OPERATOR

  • PANIGRAHI, TRAILOKYA
    • Journal of the Korean Mathematical Society
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    • v.53 no.1
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    • pp.147-159
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    • 2016
  • In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

Differential Subordination and Superordination Results associated with Srivastava-Attiya Integral Operator

  • Prajapat, Jugal Kishore;Mishra, Ambuj Kumar
    • Kyungpook Mathematical Journal
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    • v.57 no.2
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    • pp.233-244
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    • 2017
  • Differential subordination and superordination results associated with a generalized Hurwitz-Lerch Zeta function in the open unit disk are obtained by investigating appropriate classes of admissible functions. In particular some inequalities for generalized Hurwitz-Lerch Zeta function are obtained.

STRONG DIFFERENTIAL SUBORDINATION AND SUPERORDINATION OF NEW GENERALIZED DERIVATIVE OPERATOR

  • OSHAH, ANESSA;DARUS, MASLINA
    • Korean Journal of Mathematics
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    • v.23 no.4
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    • pp.503-519
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    • 2015
  • In this work, certain classes of admissible functions are considered. Some strong dierential subordination and superordination properties of analytic functions associated with new generalized derivative operator $B^{{\mu},q,s}_{{\lambda}_1,{\lambda}_2,{\ell},d}$ are investigated. New strong dierential sandwich-type results associated with the generalized derivative operator are also given.

A SUBMARTINGALE INEQUALITY

  • Kim, Young-Ho;Kim, Byung-Il
    • Communications of the Korean Mathematical Society
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    • v.13 no.1
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    • pp.159-170
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    • 1998
  • In this paper, we extend Burkholder's exponential inequality for a strong subordinate of a nonnegative bounded submartingale.

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STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS

  • Antonino Jose- A.
    • Journal of the Korean Mathematical Society
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    • v.43 no.2
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    • pp.311-322
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    • 2006
  • For the Briot-Bouquet differential equations of the form given in [1] $${{\mu}(z)+\frac {z{\mu}'(z)}{z\frac {f'(z)}{f(z)}\[\alpha{\mu}(z)+\beta]}=g(z)$$ we can reduce them to $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$ where $$v(z)=\alpha{\mu}(z)+\beta,\;h(z)={\alpha}g(z)+\beta\;and\;F(z)=f(z)/f'(z)$$. In this paper we are going to give conditions in order that if u and v satisfy, respectively, the equations (1) $${{\mu}(z)+F(z)\frac {v'(z)}{v(z)}=h(z)$$, $${{\mu}(z)+G(z)\frac {v'(z)}{v(z)}=g(z)$$ with certain conditions on the functions F and G applying the concept of strong subordination $g\;\prec\;\prec\;h$ given in [2] by the author, implies that $v\;\prec\;{\mu},\;where\;\prec$ indicates subordination.

ON A FIRST ORDER STRONG DIFFERENTIAL SUBORDINATION AND APPLICATION TO UNIVALENT FUNCTIONS

  • Aghalary, Rasoul;Arjomandinia, Parviz
    • Communications of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.445-454
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    • 2022
  • Using the concept of the strong differential subordination introduced in [2], we find conditions on the functions θ, 𝜑, G, F such that the first order strong subordination θ(p(z)) + $\frac{G(\xi)}{\xi}$zp'(z)𝜑(p(z)) ≺≺ θ(q(z)) + F(z)q'(z)𝜑(q(z), implies p(z) ≺ q(z), where p(z), q(z) are analytic functions in the open unit disk 𝔻 with p(0) = q(0). Corollaries and examples of the main results are also considered, some of which extend and improve the results obtained in [1].

Convolution Properties of Certain Class of Multivalent Meromorphic Functions

  • Vijaywargiya, Pramila
    • Kyungpook Mathematical Journal
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    • v.49 no.4
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    • pp.713-723
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    • 2009
  • The purpose of the present paper is to introduce a new subclass of meromorphic multivalent functions defined by using a linear operator associated with the generalized hypergeometric function. Some properties of this class are established here by using the principle of differential subordination and convolution in geometric function theory.

APPLICATIONS ON FOURTH-ORDER DIFFERENTIAL SUBORDINATION FOR p-VALENT MEROMORPHIC FUNCTIONS

  • Atshan, Waggas Galib;AL-Ameedee, Sarah A.;AL-Maamori, Faez Ali;Altinkaya, Sahsene
    • Honam Mathematical Journal
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    • v.43 no.3
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    • pp.513-522
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    • 2021
  • In this current study, we aim to give some applications on fourth-order differential subordination for p-valent meromorphic functions in the region U* = {z ∈ ℂ : 0 < |z| < 1} = U∖{0}, where U = {z ∈ ℂ : |z| < 1} , involving the linear operator 𝓛*pf. By making use of basic concepts in theory of the fourth-order, we find new outcomes.